Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Spring Semester | ||||
| Level of Course | 2nd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | SAMED ÖZKAN (ozkans@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| The aim of the course is to teach some concepts in Topology in detail, to create the ability of Mathematical idea and commend, to help to gain the topological knowledge and ability for their graduate educations. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Learn the concepts of sequence, net and filter. Can define the concepts of first-countable, second-countable, separable and Lindelöf space. |
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas. PO-5 Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. |
Examination |
| LO-2 | Can describe the separation axioms. Know the Urysohn’s lemma, Urysohn’s metrization theorem and Tietze’s extension theorem. |
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-5 Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. |
Examination |
| LO-3 | Learn the concepts of path, homotopy and fundamental group. |
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Sequences and Convergence in Topological Spaces, Nets, Filters and Ultrafilters, First-Countable and Second-Countable Spaces, Separability and Lindelöf Spaces, Separation Axioms, Hausdorff ve Regular Spaces, Tychonoff Spaces ve Normal Spaces, Urysohn’s Lemma, Urysohn’s Metrization Theorem, Tietze’s Extension Theorem, Connectedness, Path Connectedness, Homotopy, Fundamental Groups. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Sequences and Convergence in Topological Spaces | Lecturing |
| 2 | Nets, Filters and Ultrafilters | Lecturing |
| 3 | First-Countable and Second-Countable Spaces | Lecturing |
| 4 | Separability and Lindelöf Spaces | Lecturing |
| 5 | Separation Axioms | Lecturing |
| 6 | Hausdorff ve Regular Spaces | Lecturing |
| 7 | Tychonoff Spaces ve Normal Spaces | Lecturing |
| 8 | mid-term exam | |
| 9 | Urysohn’s Lemma | Lecturing |
| 10 | Urysohn’s Metrization Theorem | Lecturing |
| 11 | Tietze’s Extension Theorem | Lecturing |
| 12 | Connectedness | Lecturing |
| 13 | Path Connectedness | Lecturing |
| 14 | Homotopy | Lecturing |
| 15 | Fundamental Groups | Lecturing |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | O. Mucuk, Topoloji ve Kategori, Nobel Yayın, Ankara, 2010. | |
| 2 | J. R. Munkres, Topology (Second Edition), Prentice-Hall, Saddle River NJ, 2000. | |
| 3 | M. Koçak, Genel Topolojiye Giriş ve Çözümlü Alıştırmalar, Kampüs Yayıncılık, Eskişehir, 2011. | |
| 4 | S. Lipschutz, General Topology, Schaum’s Outline Series, New York, 1965. | |
| Required Course instruments and materials | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 16 | 2 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 3 | 14 | 42 |
| Outside Class | |||
| a) Reading | 5 | 14 | 70 |
| b) Search in internet/Library | 2 | 14 | 28 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 4 | 4 | 16 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 5 | 4 | 20 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 180 | ||